EXAM 1 90148-exm-07

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90148 Level 1 Mathematics, 2007 90148 Sketch and interpret graphs © New Zealand Qualifications Authority, 2007 All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority. 1 For Assessor’s use only Achievement Criteria Achievement Achievement with Merit Achievement with Excellence Sketch, and interpret features of, graphs. Sketch, and interpret features of, graphs. Determine and apply an appropriate model for a situation involving graphs. Write equations for linear graphs. Overall Level of Performance (all criteria within a column are met) Credits: Three 9.30 am Tuesday 20 November 2007 Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page. You should answer ALL the questions in this booklet. You should show ALL working. If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question. Check that this booklet has pages 2–14 in the correct order and that none of these pages is blank. YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION. For Supervisor’s use only 901480

Transcript of EXAM 1 90148-exm-07

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Level 1 Mathematics, 200790148 Sketch and interpret graphs

© New Zealand Qualifications Authority, 2007All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.

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For Assessor’s use only Achievement Criteria

Achievement Achievement with Merit

Achievement with Excellence

Sketch, and interpret features of, graphs.

Sketch, and interpret features of, graphs.

Determine and apply an appropriate model for a situation involving graphs.

Write equations for linear graphs.

Overall Level of Performance (all criteria within a column are met)

Credits: Three9.30 am Tuesday 20 November 2007

Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.

You should answer ALL the questions in this booklet.

You should show ALL working.

If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.

Check that this booklet has pages 2–14 in the correct order and that none of these pages is blank.

YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.

For Supervisor’s use only

901480

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You are advised to spend 30 minutes answering the questions in this booklet.

QUESTION ONE

Use the grids alongside to draw the graphs of:

(a)

y x= −13 2

y

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(b) x = – 3 y

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(c) y = x(x – 2) y

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Note: If you need to redraw any of these graphs, you will find blank grids on page 11.

Make sure you show which question you are answering beside each new grid used.

Make sure it is clear which graph you want marked.

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QUESTION TWO

Lynda walks from her home to the ice cream shop.Ruth runs fast from her home to the ice cream shop.Their distances, d, from the ice cream shop are shown on the graph below, where d is the distance in metres and t is the time in minutes.

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10 2 3 4 5 t (minutes)

d (metres)

(a) What is the distance of Lynda’s home from the ice cream shop?

(b) How fast (in metres per minute) did Lynda walk between her home and the ice cream shop?

(c) How long did it take Ruth to run from her home to the ice cream shop?

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(d) Write the equation for Ruth’s distance, d, from the ice cream shop.

(e) Lynda and Ruth both left home at 4.30 pm to go to the ice cream shop.

When would they be the same distance from the ice cream shop?

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QUESTION THREE

Write the equations of the lines drawn on the grid below.

(a)

(b)

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QUESTION FOUR

Sketch the following graphs on the axes below.

(a) 2y + 3x = 6 y

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(b) y = 2x2 – 8 y

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(c) y = –x(x – 1) – 2 = –x2 + x – 2

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Note: If you need to redraw any of these graphs, you will find blank grids on page 12.

Make sure you show which question you are answering beside each new grid used.

Make sure it is clear which graph you want marked.

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QUESTION FIVE

John and Richard were playing with a soccer ball.The graph shows the height of the ball above the ground, during one kick from John, J, towards Richard, R. The height of the ball above the ground is y metres.The horizontal distance of the ball from John is x metres.

The graph has the equation y = 0.1(9 – x)(x + 1).

x

y

J R

(a) Write down the value of the y-intercept and explain what it means in this situation.

y-intercept is

explanation:

(b) What is the greatest height of the ball above the ground?

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(c) Jake and Ryan are playing volleyball. Jake is 4.0 metres from the net on one side and Ryan is 1.5 metres from the net on the other

side, as shown in the diagram. When the ball is hit from one player to the other, the path of the ball can be modelled by a

parabola.

1.0 m

2.2 m

4.0 m 1.5 mRyanJake

x

ynet Diagram is

NOT to scale

The height of the ball when it leaves Jake is 1 metre above the ground. The ball reaches its maximum height of 3 metres above the ground when it is directly above

the net. When Ryan jumps, he can reach to a height of 2.2 metres.

Form an equation to model the path of the ball and use it to determine whether or not Ryan could reach it when he jumps.

You must justify your answer with clear mathematical reasoning, including showing exactly how you used the equation to obtain your answer.

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Question y

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Question y

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Use these grids if you need to redraw any of the graphs on pages 2 and 3. Make sure that you show which questions you are answering if you use these grids.

Make sure it is clear which graph you want marked.

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Question y

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Question y

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Use these grids if you need to redraw any of the graphs on pages 7 and 8. Make sure that you show which questions you are answering if you use these grids.

Make sure it is clear which graph you want marked.

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Question number

Extra paper for continuation of answers if required.Clearly number the question.

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Question number

Extra paper for continuation of answers if required.Clearly number the question.

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